class HMdcAligner: public HReconstructor

 Default constructor.

 Constructor including module election. Alignment procedure
 proyects hits of modA in modB coordinate system and compares

 Constructor including module election (and name and title, which
 seems to be very important). Alignment procedure
 proyects hits of modA in modB coordinate system and compares

 Constructor for only one MDC

 Inits common defaults

 Destructor.

 Minimization defaults

  				HGeomVector*& ang2,HGeomVector*& tra2,
  				HGeomVector*& ang3,HGeomVector*& tra3)

 Serves pointers to the relative transformation parameters


    if (fNumMods>3){
    ang3 = &fEuler[2];         //MDC A - MDC D
    tra3 = &fTranslation[2];
    ang2 = &fEuler[1];         //MDC B - MDC D
    tra2 = &fTranslation[1];
    ang = &fEuler[0];          //MDC C - MDC D
    tra = &fTranslation[0];
    if(A_DEBUG>2){
    cout << " HMdcAligner :: getRelParams(). Filling " << endl;
    cout << "ang3: " << ang3 << endl;
    cout << "tra3: " << tra3 << endl;
    cout << "ang2: " << ang2 << endl;
    cout << "tra2: " << tra2 << endl;
    cout << "ang: " << ang << endl;
    cout << "tra: " << tra << endl;
    }
    }
    else if(fNumMods>2){
    ang2 = &fEuler[1];          //MDC A - MDC C
    tra2 = &fTranslation[1];
    ang = &fEuler[0];           //MDC B - MDC C
    tra = &fTranslation[0];
    if(A_DEBUG>2){
    cout << " HMdcAligner :: getRelParams(). Filling " << endl;
    cout << "ang2: " << ang2 << endl;
    cout << "tra2: " << tra2 << endl;
    cout << "ang: " << ang << endl;
    cout << "tra: " << tra << endl;
    }
    }
    else{
    ang = &fEuler[0];           //MDC A - MDC B
    tra = &fTranslation[0];
    if(A_DEBUG>2){
    cout << " HMdcAligner :: getRelParams(). Filling " << endl;
    cout << "ang: " << ang << endl;
    cout << "tra: " << tra << endl;
    }
    }

 Sets ascii output for debugging.

 Sets ascii output for debugging.

 Sets number of sigmas in cuts.

 Sets the Tukey constant in the weigth determination
 for 1 MDC target finder

 Sets Local Target position for the module where is not defined
 (that is, for the MDC in first position in the constructor).
 Requires the definition and use of the target on the module
 (WARNING: Use it only for 2 MDCs up to now.
 It is mandatory to enter in the second position in the
 constructor the MDC where the target is defined from)

 Sets the center coordinates and side lengths of the rectangles
 where tracks are accepted for studying rotations

ZONES
 Every rectangular zone is defined around (x,y) with side (dx,dy).
(tested in macros)
i.e. Int_t zones_X[9] = {-500,0,500,-400,0,400,-250,0,250}
     Int_t zones_Y[9] = {400,400,400,-100,-100,-100,-600,-600,-600}
     Int_t zones_DX[9] = {150,150,150,100,100,100,50,50,50}
     Int_t zones_DY[9] = {150,150,150,100,100,100,50,50,50}
Suggested with symmetrical (extreme) values
p.e.MDCII
     Int_t zones_X[9] = {-200,0,200,-200,0,200,-200,0,200}
     Int_t zones_Y[9] = {200,200,200,0,0,0,-200,-200,-200}
     Int_t zones_DX[9] = {100,100,100,75,75,75,40,40,40}
     Int_t zones_DY[9] = {100,100,100,75,75,75,40,40,40}
p.e.MDCIII
     Int_t zones_X[9] = {-350,0,350,-350,0,350,-350,0,350}
     Int_t zones_Y[9] = {350,350,350,0,0,0,-350,-350,-350}
     Int_t zones_DX[9] = {150,150,150,100,100,100,60,60,60}
     Int_t zones_DY[9] = {150,150,150,100,100,100,60,60,60}
p.e.MDCIV
     Int_t zones_X[9] = {-400,0,400,-400,0,400,-400,0,400}
     Int_t zones_Y[9] = {400,400,400,0,0,0,-400,-400,-400}
     Int_t zones_DX[9] = {200,200,200,150,150,150,100,100,100}
     Int_t zones_DY[9] = {200,200,200,150,150,150,100,100,100}

 Inits histograms

Fits to a gaussian the four relevant histograms
and obtains the fit parameters for further data selection
Only valid for two MDCs or three MDCs

 Inits TNtuple

 Inits hitaux category and calls setParContainers()

 Call the functions returning auxiliar geometrical parameters

Turn on the fCloseToSolution flag to introduce better fits

Turn on the automatic geometrical parameter input
Use it for inserting manually the parameters in the macro

 Disables control histograms output (saving memory)

 Selects minimization strategy

 select = 0  Disables minimization
 select = 1  Angle reduction by minuit
 select = 2  Analytic translation minimization
 select = 3  (1+2) Angle reduction+analytic translation
 select = 4  Translation reduction by minuit
 select = 5  6 parameters reduction by minuit
 select = 10 Pure geometrical rotation finder
 select = 11 Translation finder before and after select=10
 select = 12 Translation finder between steps in select=10
 select = 14 Pure rotation determination by sampling
 select = 15 Translation finder before and after select=14
 select = 16 Translation finder between steps in select=14

 select = 500 + (10,11,12,14,15,16) Iterative minimization
            version of the previously described algorithms

 select = 100 (fcnalign34) Chi square sum in minimization
 select = 101 (fcnalign34) Distances line-hit

 select = 105 (fcnalign34) Minimizing angles between 2 lines
              made from Hits (testing)
 select = 106 (fcnalign34) Error with MINOS!

 select = 777 Testing the contour

 select = 200 ROTATION FINDER USING MINUIT (testing)

 introduce unit errors in Hits

 Sets off the covariance in the translationFinder() function

 Sets off the covariance in fitHistograms()

 Target position is defined and used for
 the hit definition in
 (WARNING: Use it only for 2 MDCs up to now.
 It is mandatory to enter in the second position in the
 constructor the MDC where the target is defined from)

Discart Hits in overcrowded zones to create a (quasi)homogeneous
distribution

 Fix a parameter set in minimization
 New scheme: 18 bits (binary number) specifying the parameters
 fixed (1) and released (0). Lower bit is first parameter

 Disables the cuts after fitting the histograms

 Enables the cuts in the Geometrical determination
 of rotations around X or Y axis

 Enables the cuts in the Geometrical determination
 of rotations around X or Y axis

 Disables the use of zones in the different
 rotation finders. Instead of zones weigthed hits are used

 Enables the Slope cuts after fitting the histograms.
 This cut makes the sample near indep. of Z translations
 and results useful for X and Y minimization.
 For 2 MDCs: the cut is effective only in MDCB, because fTranslation
 is represented in MDCB coordinates. Then, tracks passing
 the cut are almost parallel to Z direction if fSlopeCut is positive
 For 3 MDCs: a mean value for the three slopes. tracks passing
 the cut are almost parallel to Z direction if fSlopeCut is positive

 Loads the parameter containers it uses later

 Defines the parameter containers it uses later

 The transformations are:  X = R X' + T
 in the geometrical parameters.
 To obtain relative transformations: X(B) = M X(A) + V
 we follow:
   X = R(A) X(A) + T(A)
   X = R(B) X(B) + T(B)

   X(B) = [R(B)]E-1 R(A) X(A) + [R(B)]E-1 [T(A)-T(B)]

   M = [R(B)]E-1 R(A)
   V = [R(B)]E-1 [T(A)-T(B)]

 From M it is easy to get the relative Euler angles

 CONVENTION: fRotMat[i] and fTranslation[i] store the
 matrix M and vector V of the transformations made like this:
 4 modules: [0]  X(D) = fRotMat[0] X(C) + fTranslation[0]
            [1]  X(D) = fRotMat[1] X(B) + fTranslation[1]
            [2]  X(D) = fRotMat[2] X(A) + fTranslation[2]

 3 modules: [0]  X(C) = fRotMat[0] X(B) + fTranslation[0]
            [1]  X(C) = fRotMat[1] X(A) + fTranslation[1]

 2 modules: [0]  X(B) = fRotMat[0] X(A) + fTranslation[0]

 From the relative rotation, get the euler angles (radians)

 From an Euler rotation (see Dahlinger paper for the convention)
 the euler angles are:
 euler[0] = atan2(rot(5)/sin(euler[1]),rot(2)/sin(euler[1]))
 euler[1] = acos (rot(8))    with possible change of sign
 euler[2] = atan2(rot(7)/sin(euler[1]),-rot(6)/sin(euler[1]))

 Entering geometrical parameters.

 To be used introducing in the macro the parameters for
 testing, optimization ...

 Iteration in the hit category. Fills histograms
 and TTree and calculates relevant quantities

 New execute for four MDCs
 Find the projection of Hits in the most external MDCs
 on the inners (besides this can be modified, changing the
 order of the MDCs in the constructor). Then merge the hits
 and continue to find till the last MDC. If successfull,
 fills a TClonesArray of Hits in a TTree for further
 analysis and minimization

 New execute for more than two MDCs

 Adapting the old execute

 Only one MDC. Trying to find out the point where all
 tracks point to.

 Transformation from one coordinate system to a new one
     newV = eulrot * oldV + eulvec
 (NOT USED)

 Transformation from one coordinate system to a new one
     newV = eulrot * (oldV - eulvec)
 (NOT USED)

 Find the projection point of a Hit on another MDC

 Given a relative rotation and translation from MDC A to MDC B
 (see CONVENTION in HMdcAligner::setGeomAuxPar())
  X(B) = rot X(A) + tra
 this function obtains the projection in MDC B of a Hit in MDC A

 When the user wants to obtain the projection in MDC A of a Hit in
 MDC B, should provide the inverse transformations
 Example: X(A) = rot-1 * X(B) - rot-1 * tra
               = newrot * X(B) + newtra
 where:
    newrot = rot-1
    newtra = - (rot-1 * tra)
 The function returns also the slopes in the new coordinate system

Check if the hit is inside a window around point and slope
old check based on square cuts
New one based on equiprobability elipse (Beatriz paper)

 Propagates hitA in hitB coordinate system and merges
 the information in a new hit in hitB coordinate system
 The rot and tra verifies the CONVENTION
 (see HMdcAligner::setGeomAuxPar()), that is:
     X(B) = rot X(A) + tra
 Normally B is reference MDC, which is farther from target
HMdcHit* pHit = new HMdcHit();
Now, only mean values. Later, propagate the covariance and add the
multiple scattering effect on hitA

      pHit->setX(,);
      pHit->setY(,);
      pHit->setXDir(,);
      pHit->setYDir(,);

      return pHit;

Only for test purposes, return hitB
  return hitB;
Testing a merge in function of the coordinates

Transform hit angular components in slopes

 Getting module A parameters from module B parameters (fRotLab fTransLab)
 and from relative parameters (fRotMat and fTranslation)
 The transformations are:  X = R X' + T
 in the geometrical parameters. We have here:
   X = R(B) X(B) + T(B)
 and we know
   X(B) = M x(A) + V
 where
   M = [R(B)]E-1 R(A)
   V = [R(B)]E-1 [T(A)-T(B)]
 are the relative transformations we know (see HMdcAligner)
 We want to find out the transformation
   X = R(A) X(A) + T(A)
 using:
   X = R(B) X(B) + T(B) = R(B) (M x(A) + V)  + T(B) =>
   X = R(B) M x(A) + R(B) V  + T(B) =>
   R(A) = R(B) M  and
   T(A) = R(B) V  + T(B)

 Statistical information and Minimization procedure

 Performs the graphical output from obtained parameters

 Stores all histos and tree in the Root file

 Fill a matrix using the Euler angles of the relative transformation

OLD
      fRotMat[0][0]=(cos(prim) * cos(segu) * cos(terc)) - (sin(prim) * sin(terc));
      fRotMat[1][0]=( - cos(prim) * cos(segu) * sin(terc)) - (sin(prim) * cos(terc));
      fRotMat[2][0]=(cos(prim) * sin(segu));
      fRotMat[0][1]=(sin(prim) * cos(segu) * cos(terc)) + (cos(prim) * sin(terc));
      fRotMat[1][1]=( - sin(prim) * cos(segu) * sin(terc)) + (cos(prim) * cos(terc));
      fRotMat[2][1]=(sin(prim) * sin(segu));
      fRotMat[0][2]=( - sin(segu) * cos(terc));
      fRotMat[1][2]=(sin(segu) * sin(terc));
      fRotMat[2][2]=(cos(segu));

ATT! Correspondencia entre HGeomRotation y la antigua transf. arriba

  rot(0) rot(1) rot(2)     fRotMat[0][0] fRotMat[1][0] fRotMat[2][0]
  rot(3) rot(4) rot(5)  =  fRotMat[0][1] fRotMat[1][1] fRotMat[2][1]
  rot(6) rot(7) rot(8)     fRotMat[0][2] fRotMat[1][2] fRotMat[2][2]

 Translation from MDC A to MDC B

 Euler angles in transformation from MDC A to MDC B

 Limits of the square defined in the search procedure

 Set the criteria for iteration in the minimization (see finalize())

 Set the weights in the fcn()

 Set the module errors in the fcn()

 Set the steps in the minimization

 Set the criteria for iteration in the minimization (see finalize())

if angleIter==1 work on X, if angleIter==2 work on Y

 Copy of translation Finder for Zones

 Iterative call to the translationFinder algorithm for different
 accepted Hit distributions

 Analytical minimization of the function
 X and Y residuals
 Results are the relative translation
 vector components

 Matrix:

    a 0 c      translation[0]     f
    0 b d   *  translation[1]  =  g
    c d e      translation[2]     h

 results in

 translation[0] = (fbe+gdc-bch-fdd)/(abe-bcc-add)
 translation[1] = (age+fdc-gcc-dha)/(abe-bcc-add)
 translation[2] = (abh-fbc-gda)/(abe-bcc-add)

 Parameters can now be introduced to find the translation for
 reduced set of hits, those between lower and upper limits in
 each direction, selectable in the first param:
 XYorBoth=-1 No Cut           XYorBoth=0 Cut on X
 XYorBoth=1 Cut on Y          XYorBoth=2 Cut on both

 Divide in several zones and find for each one
 the mean residual position
 See setZones() for the definition

 Finding the rotation in local XY plane (around local Z)

 Finding the rotation in local XZ plane (around local Y)
 or around local YZ plane (around local X)
 If second argument=0, then rotations around local Y are found

 Minuit menu
 Argument fix correspon to fFix value (see setFix())
 Other arguments are init values for the parameters!

 Minuit menu for rotations
 Arguments are init values for the parameters!